Nominations officially opened for the IMF's next managing director with the aim of replacing Dominique Strauss-Kahn, who faces sexual assault charges in New York, by June 30.
Lagarde, France's finance minister, told US television network CNBC that it was "premature" to talk of her taking the job.
But a steamroller of support for her candidacy for one of the most powerful jobs in global finance was building in Europe.
Mexico's Finance Minister Ernesto Cordero lobbied for Carstens as a viable emerging economy candidate for the position, which has been monopolized by Europeans since 1946.
"We're promoting an appointment based on merit so that the IMF has the legitimacy and credibility it needs to deal with the international situation," Cordero said at a joint news conference with Carstens.
Carstens, a 52-year-old former finance minister, played up his experience with the international lender, where he worked as executive director from 1999-2000 and deputy managing director from 2000-2003.
"I know the fund from all possible angles," said Carstens, who has a doctorate from the University of Chicago.
The IMF, the lender of last resort for economies in trouble, has moved swiftly to fill the power vacuum left by Strauss-Kahn's resignation last week to face sexual assault charges in New York.
The Fund said Friday that nominations would close on June 10, and the decision should be taken within three weeks.
Other candidates being mentioned Monday included Belgium's Finance Minister Didier Reynders, South African ex-finance chief Trevor Manuel and the central bank chief of Kazakhstan, Grigori Martchenko.
The acting managing director, American John Lipsky, praised Lagarde as "a very talented and experienced leader."
"She has done an excellent job as finance minister and I'm sure she would be an excellent managing director," he said.
But he noted that "a number" of candidates have been mentioned.
"I'm blessed to say all seem to be excellent names," added Lipsky.
The exit of former French politician Strauss-Kahn, who is under house arrest in New York and denies the allegations, has exposed fault lines in the 187-nation institution.
Emerging markets, their economic weight rising, want the end of a gentleman's agreement that has kept a European heading the IMF and an American in charge of the World Bank.
But emerging economies have not coalesced around a single candidate.
Brazil's Finance Minister Guido Mantega called for more time to consider the possibilities.
South Africa's Manuel, a rumored candidate for the job, hesitated to commit.
"There are all kinds of issues. I think that for any candidate it's fundamentally important to do what the Europeans are doing, to build a critical mass of support," he said.
With three of its periphery countries in crisis and undergoing joint IMF-EU bailouts, Europe is making a strong case for one of their own to continue in the job.
The European Union could announce its candidate at the two-day Group of Eight summit in Deauville, France, that opens Thursday.
Lagarde is "practically a shoo-in," an EU source said.
But the 55-year-old also has to get past a potential legal problem -- a probe into her handling of a dispute involving tycoon Bernard Tapie and Credit Lyonnais that led to a 2008 ruling in Tapie's favor worth hundreds of millions of euros.
In the past three days, she picked up support from the Germans, British and Dutch.
"It is extremely important for Europe to have a single candidate, and it would be very good if it were Christine Lagarde," said Dutch Finance Minister Jan Kees de Jager.
New Zealand Prime Minister John Key also backed a "super impressive" Lagarde.
Belgium's Reynders offered himself as a possible solution if legal problems ensnare her.
"When, like me, you have sat around the table at the International Monetary Fund for 12 years, and have experience as finance minister, of course it would be an interesting job, a job where one could have an impact on economics and politics," he said.
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